Thanks for the question. The answer is, it would depend on several
factors-the brightness of the sun on a particular day (influenced by
clouds and the height of the sun in the sky), how long you were to stare
and of course, if you observed with the naked eye or using a
telescope/binoculars.

If you were using the last method, you would be very foolish. A piece of
paper held at the eyepiece of a telescope focused on the sun will catch
fire almost instantly-as would the front of your eyeball if you were to
look into the eyepiece. But as you correctly say, looking at the sun with
the naked eye is also very dangerous. The sun emits both infrared (heat)
and ultraviolet radiation, both of which would be focused and concentrated
onto your retina if you were to stare at the sun. In bright sunlight, the
cells at that point on your retina could be damaged beyond repair in a few
seconds. In addition, your retina contains a region of very sensitive
cells called the yellow spot or fovea. This is responsible for the
ability to detect fine details at low light levels and destruction of
these cells causes substantial visual impairment.

So, the brief answer to your question is "anywhere from almost instantly
to a very few seconds". And remember also there are no pain receptors in
the retina, so you wouldn't even know it had happened. I'm sure you know
already, but we really can't stress enough the importance of not looking
directly at the sun for any length of time, ever, ever, ever. It's
incredibly dangerous.